Is battery life better on the iPhone 5s?

Has it improved since the 4s?

Apple uses the same "slab" battery for all iphones. Most of them are only around 1.3 amp hours and still considered disposable. What i'm saying here: don't expect the battery life to change from the 4s to the 5s.

the battery life depends greatly on backlight use, screen brightness and running programs.

5S is far better then 4S battery, actually the hardware all around is far better on 5S

Definitely.

I wouldn't say so. I have family memebers who have both and honestly they hate it they have to plug it at the wrong time everytime they go out by the time they're not even drunk yet their phone is dead.